Question

A machine depreciates at the rate of $10\%$ of its value at the beginning of a year. If the present value of a machine is $\text{Rs.}4000$, find its value after $3$ years.

• A. $\text{Rs.}1916$
• B. $\text{Rs.}2916$
• C. $\text{Rs.}3916$
• D. $\text{Rs.}4916$

Answer 1

The correct option is B $\text{Rs.}2916$

Given:-

$P=\text{Rs.}4000$

$r=10\%$

$n=3$ years

Now, as the value of the machine depriciates every year by $10\%,$

$\begin{array}{cc}A& =P{\left(1-\frac{r}{100}\right)}^n\\ & =4000{\left(1-\frac{10}{100}\right)}^3\\ & =4000{\left(0.9\right)}^3\\ & =\text{Rs.}2916\end{array}$

Hence, the value of the machine after $3$ years is $\text{Rs.}2916.$